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Dipartimenti e Istituti di Scienze Economiche

Long-run Phillips Curve and Disinflation Dynamics: Calvo vs. Rotemberg Price Setting

Guido Ascari Lorenza Rossi

IEF0082 - September - 2008

UNIVERSITA’ CATTOLICA DEL SACRO CUORE - Milano -

QUADERNI DELL’ISTITUTO DI ECONOMIA E FINANZA


Guido Ascari Lorenza Rossi

n. 82 - settembre 2008

Quaderni dell’Istituto di Economia e Finanza numero 82 settembre 2008


Guido Ascari (°) Lorenza Rossi (*)

(°)Università degli Studi di Pavia e IfW (*)Istituto di Economia e Finanza, Università Cattolica del Sacro Cuore, Largo Gemelli 1 – 20123 Milano, e-mail: [email protected]

Comitato Scientifico Redazione Dino Piero Giarda Istituto di Economia e Finanza Michele Grillo Università Cattolica del S. Cuore Pippo Ranci Largo Gemelli 1 Giacomo Vaciago 20123 Milano tel.: 0039.02.7234.2976 fax: 0039.02.7234.2781 e-mail: [email protected] * Esemplare fuori commercio per il deposito legale agli effetti della Legge n. 106 del 15 aprile 2004. * La Redazione ottempera agli obblighi previsti dalla Legge n. 106 del 15.04.2006, Decreto del Presidente della Repubblica del 03.05.2006 n. 252 pubblicato nella G.U. del 18.08.2006 n. 191. * I quaderni sono disponibili on-line all’indirizzo dell’Istituto http://www.unicatt.it/istituti/EconomiaFinanza * I Quaderni dell’Istituto di Economia e Finanza costituiscono un servizio atto a fornire la tempestiva divulgazione di ricerche scientifiche originali, siano esse in forma definitiva o provvisoria. L’accesso alla collana è approvato dal Comitato Scientifico, sentito il parere di un referee.

Long-run Phillips Curve and Disin�ationDynamics: Calvo vs. Rotemberg Price Setting

Guido AscariUniversity of Pavia and IfW

Lorenza RossiCatholic University of Milan

June 2008

Abstract

There is widespread agreement that the two most widely usedpricing assumptions in the New-Keynesian literature, i.e., Calvo andRotemberg price-setting mechanisms, deliver equivalent dynamics. Weshow that, instead, they entail a very di¤erent dynamics of adjustmentafter a disin�ation, once non linear simulations are employed. In theCalvo model disin�ation implies output gains, while in the Rotembergmodel a disin�ation experiment implies output losses. We show thatthis is due to the di¤erent wedges created by the nominal rigidities inthe two models: between output and hours in the Calvo model, whilebetween output and consumption in the Rotemberg model. More-over, unlike the Calvo model, in the Rotemberg model real wage rigidi-ties cause a signi�cant output slump along the adjustment path, thusrestoring a dynamics in line both with the conventional wisdom andthe empirical evidence.

JEL classi�cation: E31, E5.

Keywords: Disin�ation, Sticky Prices, Nonlinearities

1 Introduction

In this paper, we consider the standard New Keynesian framework of mo-nopolistically competitive �rms with two commonly used approaches tomodel �rms�price-setting behavior: the Rotemberg (1982) quadratic costof price adjustment and the Calvo (1983) random price adjustment signal.The Calvo price-setting mechanism produces relative-price dispersion among�rms, while the Rotemberg model is consistent with a symmetric equilib-rium. Despite the economic di¤erence between these two pricing speci�ca-tions, to a �rst order approximation the implied dynamics are equivalent.As shown by Rotemberg (1987) and Roberts (1995), both approaches implythe same reduced form New Keynesian Phillips curve (NKPC henceforth).1

They therefore lead to observationally equivalent dynamics for in�ation andoutput. In particular, both models deliver the well-known result of im-mediate adjustment of the economy to the new steady state following adisin�ation, despite nominal rigidities in price-setting (see, e.g., Ball, 1994and Mankiw, 2001). Furthermore Nisticò (2007), shows that up to a sec-ond order approximation, and provided that the steady state is e¢ cient,both models imply the same welfare costs of in�ation. Thus, they imply thesame prescriptions for welfare-maximizing Central Banks. Therefore, thereis widespread agreement in the literature that the two models are equivalent.

In this work, we show that it is not the case when permanent changesin the rate of in�ation are considered, if one takes into account the full non-linear model. In particular, the long-run Phillips curve implied by the twomodels is radically di¤erent. As a consequence, the non-linear disin�ationdynamics implied by the two model is also very di¤erent. As some papershave recently demonstrated (e.g. Ascari 2004, Yun 2005, Ascari and Merkl2007) non-linearities are important because of the interaction between long-run e¤ects and short-run dynamics in the non-linear dynamics of the model.Contrary to the common view, this interaction leads to completely di¤erentresults between the implied non-linear dynamics by the Rotemberg and theCalvo price setting speci�cations in response to a Central Bank disin�ationexperiment.

Ascari and Merkl (2007) shows that non-linearities are important inshaping the adjustment dynamics following a disin�ation in a Calvo pricesetting model. Indeed, contrary to the dynamics implied by the traditionallog-linearized Calvo model, a disin�ation leads to a permanently higher level

1Kahn (2005), however, shows that even if the reduced form New Keynesian Phillipscurve is the same, the impact of competition on the slope of the NKPC and on the responseof in�ation and output to shocks di¤ers between the two approaches.

1

of output in the non-linear model, with no slump. Moreover, according tothe conventional view, real wage rigidities should generate a slump in outputafter a credible disin�ationary policy, because they prevent the immediateadjustment of in�ation. However, Ascari and Merkl (2007) shows that inthe non-linear Calvo model real wage rigidities increase the output duringthe adjustment to the new steady state. Real wage rigidities may even leadto an overshooting of the output above the new higher steady state level. Aresult which thus seems to be strongly at odds with the conventional view.

Unlike the Calvo model, we show that the non-linear dynamics of theRotemberg price setting model restores results similar to the log-linear dy-namics. First of all, output immediately adjust to an immediate and un-expected disin�ation. Secondly, real wage rigidities imply a signi�cant out-put slump along the adjustment path, restoring a conventional result onwhich there seems to be consensus in the literature (see, e.g., Blanchardand Galí, 2007). In sum, inferring the e¤ects of permanent shocks throughlog-linearized model would not lead to big mistakes, as in the Calvo model.Therefore, the Rotemberg model seems to be more robust to non-linearities.

2 The model and the long-run Phillips Curve: Calvo(1983) vs. Rotemberg (1982)

In this section we brie�y present a very simple and standard cashless NewKeynesian model in the two version of Rotemberg and the Calvo price settingscheme. We then look at the long-run features of the two models, and inparticular, at the implied long-run Phillips Curve.

2.1 The model

2.1.1 Households and Technology

Consider an economy with a representative household which maximizes thefollowing intertemporal separable utility function:

Et

1Xj=0

�j

"C1��t+j

1� � � dnN1+'t+j

1 + '

#(1)

subject to the period-by-period budget constraint

PtCt + (1 + it)�1Bt =WtNt � Tt +�t +Bt�1, (2)

2

where Ct is consumption, it is the nominal interest rate, Bt are one-periodbond holdings, Wt is the nominal wage rate, Nt is the labor input, Tt arelump sum taxes, and �t is the pro�t income. The following �rst orderconditions hold:

Euler equation :1

C�t= �Et

��PtPt+1

�(1 + it)

�1

C�t+1

��, (3)

Labor supply equationWt

Pt= �UN

UC=dnN

't

1=C�t= dnN

't C

�t . (4)

Final good market is competitive and the production function is givenby

Yt =

�Z 1

0Y

"�1"

i;t di

� ""�1

: (5)

Final good producers demand for intermediate inputs is therefore equal to

Yi;t+j =�Pi;tPt+j

��"Yt+j .

Intermediate inputs Yi;t are produced by a continuum of �rms indexedby i 2 [0; 1] with the following simple technology

Yi;t = N1��i;t (6)

where labor is the only input and 0 � � < 1. The labor demand and thereal marginal cost of �rm i are therefore

Ndi;t = [Yi;t]

11�� , (7)

and

MCri;t =1

1� �Wi;t

PtY

�1��i;t : (8)

Note that, given the possibility of decreasing returns to labor, if � > 0;then di¤erent �rms charging di¤erent prices would produce di¤erent levelsof output and hence have di¤erent marginal costs

MCri;t =1

1� �Wi;t

Pt

"�Pi;tPt

��"Yi;t

# �1��

: (9)

Each �rm i has monopolistic power in the production of its own variety andtherefore solves a price setting problem.

3

2.1.2 Price Setting: Calvo (1983) vs. Rotemberg (1982)

The Calvo modelWe will here show a generalized version of the Calvo price setting scheme,allowing for indexation. In each period there is a �xed probability 1 � �that a �rm can re-optimize its nominal price, i.e., P �i;t: With probability �,instead, the �rm automatically and costlessy adjust its price according toan indexation rule. The price setting problem becomes

maxfYi;t;Pi;tg1t=0

Et

1Xj=0

�j�t+j�0

�j

24P �i;t ��j�1��t;t+j�1

��Pt+j

Yi;t+j �Wt+j

Pt+j[Yi;t+j ]

11��

35 ,

s.t. Yi;t+j =

24P �i;t ��j�1��t;t+j�1

��Pt+j

35�" Yt+j and (10)

�t;t+j�1 =

( �PtPt�1

��Pt+1Pt

��

�Pt+j�1Pt+j�2

�for j = 1; 2; � � �

1 for j = 0.(11)

where � denotes the central bank�s in�ation target and it is equal to the levelof trend in�ation. This formulation is very general, because: (i) � 2 [0; 1]allows for any degree of price indexation; (ii) � 2 [0; 1] allows for any degreeof (geometric) combination of the two types of indexation usually employedin the literature: to steady state in�ation (e.g., Yun, 1996) and to pastin�ation rates (e.g., Christiano et al., 2005).

In the Calvo price setting framework, �rms charging prices at di¤erentperiods will have di¤erent prices. In general, there will be a distributionof di¤erent prices, that is, there will be price dispersion. Price dispersionresults in an ine¢ ciency loss in aggregate production. Hence

Ndt = [Yt]

11��

Z 1

0

"�Pi;tPt

��"di

#| {z }

st

11��

= [stYt]1

1�� . (12)

Schmitt-Grohé and Uribe (2007) show that st is bounded below at one, sothat st represents the resource costs due to relative price dispersion underthe Calvo mechanism. Indeed, the higher st, the more labor is needed to

4

produce a given level of output. To close the model, the aggregate resourceconstraint is simply given by

Yt = Ct: (13)

The Rotemberg modelThe Rotemberg model assumes that a monopolistic �rm faces a quadratic

cost of adjusting nominal prices, that can be measured in terms of the �nal-good and given by

'p2

Pi;t�

��t�1��(��)1�� Pi;t�1

� 1!2Yt; (14)

where 'p > 0 determines the degree of nominal price rigidity. As stressedin Rotemberg (1982), the adjustment cost looks to account for the negativee¤ects of price changes on the customer-�rm relationship. These negativee¤ects increase in magnitude with the size of the price change and with theoverall scale of economic activity, Yt. Also (14) is a general speci�cationfor the adjustment cost used by, e.g., Ireland (2007), among others. Thisde�nition is the correspondent of the general speci�cation of the Calvo pricesetting scheme above, within the Rotemberg one. When � = 0 (� = 1) �rms�nd it costless to adjust their prices in line with the central bank in�ationtarget (the previous period�s in�ation rate). � instead plays the same roleof the degree of indexation in the Calvo model above:

The problem for the �rm is then

maxfYi;t;Pi;tg1t=0

Et

1Xj=0

�j�t+j�0

8><>:Pi;t+jPt+j

Yi;t+j � Wt+j

Pt+j[Yi;t]

11�� +

�'p2

�Pi;t+j

(��t+j�1)�(��)1��Pi;t+j�1

� 1�2Yt+j

9>=>; ;s.t. Yi;t+j =

�Pi;t+jPt+j

��"Yt+j :

The Rotemberg model is very di¤erent from the Calvo one because there isno price dispersion. Firms can change their price in each period, subject tothe payment of the adjustment cost. Therefore, all the �rms face the sameproblem, and thus will choose the same price, producing the same quantity.

In other words: Pi;t = Pt; Yi;t = Yt; and MCri;t = MCrt =1

1��WtPtY

�1��t ;

8i: Contrary to the Calvo scheme, thus, the aggregate production functionfeatures no ine¢ ciency due to price dispersion, that is

Yt = N1��t (15)

5

Indeed, in the Rotemberg model, the adjustment cost enters the aggregateresource constraint that is given by

Yt = Ct +'p2

Pt�

��t�1��(��)1�� Pt�1

� 1!2Yt; (16)

Note that this creates an ine¢ ciency wedge between output and consump-tion:

Yt

241� 'p2

Pt�

��t�1��(��)1�� Pt�1

� 1!235 = Ct (17)

This is the main di¤erence between the Calvo and the Rotemberg model.In the former one, the cost of nominal rigidities, i.e., price dispersion, cre-ates a wedge between aggregate employment and aggregate output, makingaggregate production less e¢ cient. In the Rotemberg model, instead, thecost of nominal rigidities, i.e., the adjustment cost, creates a wedge betweenaggregate consumption and aggregate output, because part of the outputgoes in the price adjustment cost.

2.2 The long-run Phillips Curve

The Calvo (1983) modelThis section looks at the steady state of the two models, and in particular

at the implications for the long-run Phillips Curve.

- Figure 1 about here -

Figure 1 shows the long-run relationship between in�ation and output inthe standard Calvo model with no indexation (i.e., � = 0).2 As well-known(e.g., Ascari 2004, Yun 2005), the long-run Phillips Curve is negativelysloped: positive long-run in�ation reduce output, because it increases pricedispersion. Higher price dispersion acts as a negative productivity shift,because Y =

�Ns

�1��. Thus, the steady state real wage lowers with trend

in�ation, and so does consumption and leisure, so that actually steady stateemployment increases. As a consequence, steady state welfare decreases.

2We consider the following rather standard parameters speci�cation (see Section 3):� = 1; � = 0:99; " = 10; � = 1; � = 0:75; � = 0 and � = 0: However, none of the resultsqualitatively depends on the parameters values.

6

To be more precise, actually, the derivative of the long-run Phillips Curveevaluated at zero in�ation, i.e., the tangent at zero in�ation of the curvedepicted in Figure 1, is positive. Indeed, this positive slope equals thepositive long-run relationship between in�ation and output implied by thestandard log-linear New Keynesian Phillips Curve popularized by Woodford(2003) among others. The positive slope is due to what Graham and Snower(2004) call the "time discounting e¤ect": in setting the new price, �rms dis-count the future, where nominal prices are higher because of trend in�ation.Hence, the average mark-up decreases with trend in�ation. However, therelationship between steady state mark-up (and thus output) and in�ationis non-linear. The e¤ects of non-linearities due to price dispersion are quitepowerful and turn up very quickly, inverting the relationship from positiveto negative.3

The Rotemberg (1982) modelThe Appendix shows that the long-run Phillips Curve in the Rotemberg

model is equal to

Y =

24 "�1" + (1��)

" 'p��1�

� � 1��1�

�

dn(1��)

�1� 'p

2 (��1�� 1)2

��35 1��'+�+�(1��)

: (18)

It follows immediately that (if � < 1)

9�� < 1 s:t:

8<:�� > �� =) dY

d�� > 0

�� = �� =) dYd�� = 0

�� < �� =) dYd�� < 0

:

Note that this implies that �� = 1 =) dYd�� > 0; so that the minimum

of output occurs at negative rate of steady state in�ation, unless � = 1.This is a "time discounting e¤ect", in the same logic of the one describedabove: in changing the price, a �rm would weight relatively more todayadjustment cost of moving away from yesterday price, than the tomorrowadjustment cost of �xing a new price away from the today�s one. As inthe Calvo model, the discounting e¤ect tends to reduce average mark-up.But unlike the Calvo model, there is no price dispersion that interact with

3Graham and Snower (2004) call these e¤ects "employment cycling" (product cyclingfor sticky prices) and "labor supply smoothing" (production smoothing for sticky prices)e¤ects. See also King and Wolman (1996).

7

trend in�ation, and thus this is the only e¤ect of trend in�ation on the pricesetting decision. Indeed, the steady state mark-up is given by

markup =

�"� 1"

+(1� �)"

'p��1�

� � 1��1�

�

��1(19)

which is monotonically decreasing in ��; for positive trend in�ation (�� > 1):The fact that the mark-up decreases with trend in�ation makes output toincrease with trend in�ation. However, a fraction of output is not consumed,but it is eaten up by the adjustment cost. As evident from (17), the ad-justment cost is increasing in trend in�ation, and so is the wedge betweenoutput and consumption. The higher trend in�ation, the more output isproduced, but the less is consumption. Opposite to the Calvo model, then,output is increasing with trend in�ation, but, as in the Calvo model, em-ployment is increasing, while consumption and welfare are decreasing withtrend in�ation (see Figure 2)4.


As we will see in the next section, the opposite slope of the long-runPhillips Curve between the two models determines a very di¤erent short-run adjustment in the non-linear dynamics following a permanent shift inthe central bank in�ation target.

3 Temporary vs. permanent shock

In this section we look at two monetary policy experiments: 1) a temporarynegative shock to the in�ation target; 2) an unanticipated and permanentreduction in the in�ation target of the Central Bank. The Central Bankfollows a standard Taylor rule, with the weight �� on deviations of in�ationfrom the target level and the weight �y on output deviations, i.e.,�

1 + it1 +�{

�=��t��

�� Yt�Y

��y. (20)

We consider the following parameters speci�cation, as in Ascari and Merkl(2007): � = 1; � = 1; � = 0:99; " = 10; 'p = 100; � = 0:75; � = 0 and

4As in Ireland (2007), we set the cost of adjusting prices 'p = 100; to generate a slopeof the log-linear Phillips curve equal to 0.10.

8

� = 0: Since the monetary authority implements the standard Taylor (1993)rule, we set �� = 1:5 and �y = 0:5: None of the qualitative results and ofthe arguments in the paper depends on the calibration values chosen.5

3.1 Temporary Shock

We now consider the dynamics of the two non linear models after a 1%temporary negative shock to the in�ation target ��:We set the autoregressiveparameter of the shock to � = 0:5: We plot the impulse response functions(IRFs henceforth) of output, in�ation, nominal interest rate, real wages andconsumption, assuming 4% trend in�ation.

The Calvo modelFigure 3 displays the IRFs to a 1% temporary negative shock to the in�a-

tion target �� when the model is based on the Calvo staggered price-setting.A negative temporary shock to the in�ation target is followed by a mone-tary tightening that causes a slump in output and a temporary reduction inin�ation, real wages, consumption and hours.


The Rotemberg modelFigure 4 shows the IRFs for the same policy experiment in the case of

the Rotemberg model. Also in this case a negative temporary shock to thein�ation target is followed by a monetary tightening. The increase in thenominal interest rate induces a fall in output and a temporary reduction inin�ation, real wages, consumption and hours.


5Figures 1-8 are obtained using the software DYNARE developed by Michel Juillardand others at CEPREMAP, see http://www.cepremap.cnrs.fr/dynare/. The paths in theFigures correspond to deterministic simulations, since they display the movement from adeterministic steady state to another one. DYNARE solves for these paths by stacking upall the equations of the model for all the periods in the simulation (which we set equal to100). Then the resulting system is solved en bloc by using the Newton-Raphson algorithm,by exploiting the special sparse structure of the Jacobian blocks. The non-linear modelthus is solved in its full-linear form, without any approximation.

9

Figures 3 and 4 therefore show that the two di¤erent price adjustment mech-anisms deliver a very similar dynamics in response to a temporary shock tothe in�ation target. The IRFs do not di¤er qualitatively and the quantita-tive di¤erences are almost marginal. Moreover, the adjustment dynamics toa temporary shock is not sensitive to non-linearities, in the sense that is nota¤ected by the level of trend in�ation, especially in the case of Rotembergmodel. Results are di¤erent when we consider a permanent shock to thein�ation target.

3.2 Permanent Shock

We now look at an unanticipated and permanent reduction in the in�ationtarget of the Central Bank. We plot the path for output, in�ation, nominalinterest rate, real wages, consumption and hours in response to such a changein the Central Bank policy regime. We consider three cases: a disin�ationfrom 4%, 6% and 8% to zero.

The Calvo modelAs shown by Ascari and Merkl (2007), when nonlinear simulations are

employed, the adjustment path of the Calvo model is completely di¤erentfrom the one obtained with the log-linear model. Unlike in the log-linearmodel, a disin�ation experiment increases the permanent steady state levelof output. In �gure 5 we plots the response of the main economic variables toa disin�ation for the three di¤erent initial values of trend in�ation. Outputincreases sluggish to the new higher steady state level. Moreover, the higheris the initial value of trend in�ation (i.e. the higher is the shock) the moresluggish is the transition of the variables to the new steady state level.Since output is entirely consumed, consumption and output show the sameadjustment path.

Note, instead, the adjustment dynamics in hours worked. Hours jumpon impact, because output increases. Moreover, there is an additional ef-fect that spurs hours, coming from price dispersion, i.e., s. The lower pricedispersion, so the less the hours that are needed for a given increase in out-put. For all the cases considered, price dispersion decreases monotonicallyto the new lower steady state level. This is why hours thus peak on im-pact, and then start decreasing. Indeed, along the adjustment, output isincreasing, while price dispersion is decreasing. From period 2 onwards, thelatter e¤ect then dominates, making aggregate production more e¢ cient andsaving hours worked, despite the rise in output. Note that the permanentdecrease of price dispersion can be interpreted as a permanent increase in

10

labor productivity, that in turn permanently increases the real wage. Realwages behavior also depend on the dynamics of hours, and thus on the jointdynamics of output and price dispersion. The adjustment in real wagesroughly follow the behavior of hours, showing however an hump shape andovershooting their new higher real long-run equilibrium level.

The Calvo model then implies that output and consumption closely movetogether, while output and hours move in opposite directions during the ad-justment, after the impact period. As explained in Section 2.1.2, in�ationin the Calvo model creates a wedge between aggregate employment and ag-gregate output, through price dispersion. The long-run gain of a disin�ationcomprises the decrease in this wedge, inducing a short-run dynamics that re-duces the gap between output and hours, by increasing output and reducinghours worked, thus increasing labor productivity and the real wage.


The Rotemberg modelWhen prices are set à la Rotemberg, even if nonlinear simulations are em-ployed, the economy would immediately adjust to the new steady state.This is a �rst important di¤erence between the Rotemberg and the Calvomodel, and it is entirely due to price dispersion. The Calvo model impliesprice dispersion, i.e., st; that is a backward-looking variable that adjustssluggishly after a disin�ation. Thus, the non-linear solution of the modelmust keep track of this state variable, and the model dynamics is inertial.The Rotemberg, instead, is symmetric, and thus it does not feature any pricedispersion. Thus, the non-linear version of the simple New Keynesian modelabove with Rotemberg pricing is completely forward-looking. The economy,hence, jumps immediately in the new steady state without any transitionaldynamics.6

A second important di¤erence regards the long-run e¤ects and the ad-justment dynamics of the variables. With Rotemberg pricing, a disin�ation

6Note that this would be the case also for the standard log-linear version of the NewKeynesian model with Calvo pricing (e.g., Woodford, 2003). Indeed, if log-linearizedaround a zero in�ation steady state, then price dispersion would not matter for the modeldynamics up to �rst-order. Moreover, if, instead, one assumes full indexation to trendin�ation, i.e., = 0 and � = 1; then both the log-linear and the non-linear model withCalvo pricing would imply immediate adjustment after a disin�ation, as the Rotembergmodel. Indeed, in case of full indexation, there is no price dispersion in steady state,whatever the value of trend in�ation. So nothing prevents the model to jump to the newsteady state, since price dispersion in this case does not have to adjust.

11

causes a drop in output. The higher the shock, the higher is the increasein �rms�markup and the larger is the fall of output. As a consequence, thefraction of output wasted for adjusting prices is lower. This is the reasonwhy consumption increases to the new higher steady state instead of de-creasing, as happens in the Calvo model. Hours and the real wage jumpdownward on impact to the new lower steady state value.

The Rotemberg model then implies that output and hours closely jumptogether, while output and consumption move in opposite directions on im-pact. Exactly the opposite of the Calvo model. As explained in Section2.1.2, in�ation in the Rotemberg model creates a wedge between aggregateconsumption and aggregate output, through the adjustment cost. The long-run gain of a disin�ation comprises the decrease in this wedge, by increasingconsumption, while output falls.


We therefore show that, when the economy is hit by a permanent and unan-ticipated in�ation target shock, the two nonlinear models, based on the twodi¤erent price setting mechanisms, show very di¤erent and opposite dynam-ics.

3.3 Real Wage Rigidities: E¤ects on Disin�ation Dynamics

Recently some authors suggest that real wage rigidities is an importantfeature that restores realistic output cost of disin�ation in a Calvo model(e.g., Blanchard and Galí, 2007). Ascari and Merkl (2007), instead, showthat studying the non-linear dynamics of the model, real wage rigiditiesactually create a boom in output, rather than a slump. Indeed, Ascari andMerkl (2007) assume the following partial adjustment model for real wagein order to introduce real wage rigidities à la Hall (2005)

Wt

Pt=

�Wt�1Pt�1

� MRS1� t ; (21)

where MRS is the marginal rate of substitution between labor supply andconsumption. For su¢ ciently high value of ; the model implies a slug-gish adjustment of real wages. Figure 7 replicates Ascari and Merkl (2007)experiment in the Calvo price setting model. Real wage rigidities have arather surprising implication on the economy dynamics when a disin�ationexperiment is implemented: they may lead to an overshooting of the output

12

above its new permanent natural level. The higher the values of ; the morelikely is the overshooting of output.

- �gure 7 about here -

The intuition is straightforward. As we saw in section 3.2, without realrigidities a disin�ation leads to a short-run overshooting of the real wageover its new higher long-run value. Real wage rigidities, instead, causes asluggish adjustment in the real wage, which therefore can not overshoot onimpact. The real wage is thus lower along the adjustment, and this spursoutput. Real wage rigidities, thus, transfer the overshooting from the realwage to output.

When �rms set their price à la Rotemberg the result is the other wayround, restoring conventional wisdom. Figure 8 shows that sluggish realwages cause an output slump along the adjustment path. The slump of out-put becomes more signi�cant the higher the parameter of real wage rigidities, .

- �gure 8 about here -

To give an intuition for these results, again we need to look at the inter-play between long-run e¤ects and the short-run dynamic adjustment in thenonlinear models. Unlike the Calvo model, in the Rotemberg model a dis-in�ation implies an immediate adjustment to a permanently lower level ofoutput, hours and real wage. Real wage rigidities again prevent the immedi-ate adjustment of the real wage, that sluggishly decreases towards the newlower long-run level. Hence, the higher the real wage rigidities, the higheris the real wage along the adjustment, and this depresses output. Hence,contrary to the Calvo model, the Rotemberg model exhibits a dynamics inline both with the conventional wisdom and the empirical evidence: realwage rigidities cause a signi�cant output slump along the adjustment path,and therefore they imply a signi�cant trade-o¤ between stabilizing in�ationand output (see, e.g., Blanchard and Galí, 2007).

13

3.4 Rotemberg model and consumption dynamics

As shown in the previous sections in the standard Rotemberg model, thecost of nominal rigidities, i.e., the adjustment cost, creates a wedge betweenaggregate consumption and aggregate output, because part of the outputgoes in the price adjustment cost, that represents a pure waste for the econ-omy. As a consequence, when the economy is hit by a negative permanentshock to the in�ation target, output co-moves with hours while consumptiongoes in the opposite direction.

This last result seems to be at odds with empirical �ndings, but it couldbe easily �xed by assuming that the adjustment costs are rebated to con-

sumers. As in the standard model,'p2

�Pt

(��t�1)�(��)1��Pt�1

� 1�2Yt is a cost

for the intermediate good producing �rm and therefore it lowers �rms pro�ts�t. If we now assume that the cost of adjusting prices is paid to the represen-

tative consumer, then,'p2

�Pt

(��t�1)�(��)1��Pt�1

� 1�2Yt enters the household

budget constraint increasing her revenues. When markets clear the house-

hold budget constraint becomes: Ct =WtN;tPt

+'p2

�Pt

(��t�1)�(��)1��Pt�1

� 1�2Yt

+�t: Therefore, substituting for the representative �rms pro�ts, �t;7 it isstraightforward to �nd that the aggregate resource constraint implies thatthe entire output is consumed, that is, Ct = Yt: The Appendix shows thatunder this assumption, the long-run Phillips Curve is still positively sloped,but the long-run e¤ects of in�ation on output are substantially lower than inthe standard Rotemberg model, since nothing is wasted for adjusting prices.Under this assumption, output co-moves both with hours and consumption,so a disin�ation would cause an immediate drop in output, consumtpion andhours. Finally, the introduction of real wage rigidities still causes a signi�-cant output slump along the adjustment path, and a similar path for bothhours and consumption.

4 Conclusion

This paper considers disin�ation dynamics in a New Keynesian model withtwo �rms�price-setting mechanisms: the Rotemberg (1982) quadratic cost ofprice adjustment and the staggered price setting introduced by Calvo (1983).

7The real pro�ts of the representative �rms are given by: �t = Yt � WtNtPt

�'p2

�Pt

(��t�1) (��)1� Pt�1

� 1�2Yt .

14

We show that, when non linear simulation are employed, the interaction be-tween long-run e¤ects and short-run dynamics leads to completely di¤erentresults under the two price settings speci�cations. If the Central Bank per-manently and credibly reduces the in�ation target, the Calvo model impliesoutput gain, rather than cost, of disin�ation. In the Rotemberg model, in-stead, output immediately adjust to the new lower steady state. We showthat this discrepancy is due to the di¤erent wedges that the cost of nom-inal rigidities creates in the two models. Moreover, in the Calvo model, ahigh degree of real wage rigidities delivers the odd result of an overshoot-ing of output above its new higher steady state level. On the contrary, inthe Rotemberg model, sluggish real wages cause a signi�cant output slumpalong the adjustment path. This last result restores a conventional resulton which there seems to be consensus in the literature (see, e.g., Blanchardand Galí, 2007).

15

5 References

Ascari, G. (2004): "Staggered Price and Trend In�ation: Some Nui-sances". Review of Economics Dynamics, vol. 7, No. 3, pp. 642-667.

Ascari, G., Merkl, C. (2007): "Real Wage Rigidities and the Cost ofDisin�ation". Journal of Money Credit and Banking, forthcoming.

Ball, L. (1994): "Credible Disin�ation with Staggered Price-Setting".American Economic Review, vol. 84, No. 1, pp. 282-89.

Blanchard O. and Galí J. (2007): "Real Wage Rigidities and the NewKeynesian Model". Journal of Money Credit and Banking, supplement tovol. 39, No. 1, 35-66.

Calvo G. A. (1983): "Staggered Prices in a Utility-Maximizing Frame-work". Journal of Monetary Economics vol. 12, No. 3, pp. 383-398.

Christiano, L. J., Eichenbaum, M., and Evans, C. L. (2005): Nomi-nal rigidities and the dynamic e¤ects of a shock to monetary policy. Journalof Political Economy, vol. 113 No. 1, pp. 1-45.

Graham, L. and D. Snower (2004): "The real e¤ects of money growth indynamic general equilibrium," Working Paper Series 412, European CentralBank.

Ireland, P. (2007): "Changes in the Federal Reserve�s In�ation Target:Causes and Consequences". Journal of Money, Credit and Banking, 2007,vol. 39, No. 8, pp. 1851-1882

Khan, H., U. (2005): "Price-setting Behaviour, Competition, and Markupshocks in the New Keynesian model". Economics Letters, vol. 87, No. 3,pp. 329-335.

King, R. G. and Wolman A., L. (1996): "In�ation Targeting in aSt. Louis Model of the 21st Century". Federal Reserve Bank of St. LouisQuarterly Review, 83-107.

Mankiw, N. G. (2001): "The Inexorable and Mysterious Tradeo¤ be-tween In�ation and Unemployment". Economic Journal, vol. 111, No. 471,pp. C45-61.

16

Nisticò S. (2007): "The Welfare Loss from Unstable In�ation", EconomicsLetters, vol. 96, No. 1, pp. 51-57.

Roberts J., M. (1995): "New Keynesian Economics and the PhillipsCurve". Journal of Money, Credit and Banking, vol. 27, No 4, pp. 975-84.

Rotemberg Julio, J. (1982): "Monopolistic Price Adjustment and Ag-gregate Output". The Review of Economic Studies, Vol. 49, No. 4., pp.517-531.

Rotemberg Julio, J. (1987): "The New Keynesian Microfoundations".NBER Macroeconomics Annual, pp. 63-129.

Schmitt-Grohe, S. Uribe, M. (2007): "Optimal Simple and Imple-mentable Monetary and Fiscal Rules". Journal of Monetary Economics,vol. 54, No. 6. pp. 1702-1725.

Woodford, M. (2003). Interest and Prices: Foundations of a Theory ofMonetary Policy. Princeton University Press.

Yun, T., (1996): "Nominal Price Rigidity, Money Supply Endogeneityand Business Cycle. Journal of Monetary Economics vol. 37, pp. 345-370.

Yun, T., (2005): "Optimal Monetary Policy with Relative Price Disper-sions". American Economic Review, vol. 95, No. 1, pp.89-109.

17

6 Technical Appendix

6.1 Household

Given the separable utility function

U (Ct (h) ; Nt (h)) =C1��t

1� � � dnN1+'t (h)

1 + '; (22)

subject to the budget constraint

PtCt + (1 + it)�1Bt =WtNt � Tt +�t +Bt�1, (23)

where it is the nominal interest rate, Bt are one-period bond holdings, Wt isthe nominal wage rate, Nt is the labor input, Tt are lump sum taxes, and �tis the pro�t income. The representative consumer maximizes the expecteddiscounted (using the discount factor �) intertemporal utility subject to thebudget constraint (23), yielding the following �rst order conditions:

Labor supply equation:

Wt

Pt= �UN

UC=dnN

't

1=C�t= dnN

't C

�t : (24)

We introduce real wage rigidities in the same way as Blanchard and Galí(2007), that is

Wt

Pt=

�Wt�1Pt�1

� MRS1� t =

�Wt�1Pt�1

� ��UNtUCt

�1� ; (25)

hence

Wt

Pt=

�Wt�1Pt�1

� (dnN

't C

�t )1�

: (26)

Euler equation:

1

C�t= �Et

��PtPt+1

�(1 + it)

�1

C�t+1

��(27)

6.2 Technology

Final good producers use the following technology

Yt =

�Z 1

0Y

"�1"

i;t di

� ""�1

: (28)

18

Their demand for intermediate inputs is therefore equal to

Yi;t =

�Pi;tPt

��"Yt: (29)

The production function of the intermediate good producers is instead givenby:

Yi;t = N1��i;t : (30)

6.3 The Rotemberg model

6.3.1 Firm�s pricing

Each �rm i has monopolistic power in the production of its own variety andtherefore has leverage in setting the price. In doing so it faces a quadraticcost of adjusting nominal prices, measured in terms of the �nished goodsand given by:

'p2

Pi;t�

��t�1��(��)1�� Pi;t�1

� 1!2Yt; (31)

where 'p > 0 is the degree of nominal price rigidity. This relationship,as stressed in Rotemberg (1982), looks to account for the negative e¤ects ofprice changes on customer-�rm. These negative e¤ects increase in magnitudewith the size of the price change and with the overall scale of economicactivity, Yt. Similarly to Ireland (2007) we denote �� the central bank�sin�ation target. �t�1 =

Pt�1Pt�2

is the aggregate in�ation level in the previousperiod. The parameter � lies between zero and one: 1 � � � 0: This meansthat the extent to which price setting is backward looking or adjust in linewith trend in�ation depends on whether � is closer to zero or one. When� = 0 �rms �nd it costless to adjust their prices in line with the centralbank in�ation target. When � is equal to 1 �rms �nd it costless to adjusttheir prices in line with the previous period�s in�ation rate. � instead playsthe same role of the degree of indexation in the Calvo model.

The problem for the �rm is to choose fPt(i); Nt(i)g1t=0 in order to max-imize its total market value given by,

maxfNi;t;Pi;tg

�i;tPi;t

= E0

1Xt=0

�t�t�0

8><>:Pi;tPtYi;t � Wi;t(j)

PtNi;t+

�'p2

�Pi;t

(��t�1)�(��)1��Pi;t�1

� 1�2

YtPt

9>=>; ;

19

subject to the demand constraint for each variable (29) and to (30). Letde�ne MCrt as the lagrangian multiplier of the production function. Thefollowing �rst order condition with respect to labor holds:

Wi;t

Pt= (1� �)MCri;tN��

i;t

= (1� �)MCri;tYi;tNi;t

= (1� �)MCri;tY� �1��

i;t ;

therefore real marginal costs can be written as:

MCri;t =1

1� �Wi;t

PtY

�1��i;t : (32)

The �rst order condition for the optimal price setting is given by,

�t�0

"(1� ")

�Pi;tPt

��" YtPt� 'p

Pi;t�

��t�1��(��)1�� Pi;t�1

� 1!

Yt��t�1

��(��)1�� Pi;t�1

#+

+�t�0MCri;t"

�Pi;tPt

��("+1) YtPt+

+�Et�t+1�0

'p

Pi;t+1

(��t )�(��)1�� Pi;t

� 1!

YtPi;t+1

(��t )�(��)1�� Pi;t2

= 0:

Imposing the symmetric equilibrium we get

1� 'p

Pt�

��t�1��(��)1�� Pt�1

� 1!

Pt��t�1

��(��)1�� Pt�1

+

+'p�Et

��t+1�t

�" Pt+1

(��t )�(��)1�� Pt

� 1!

Pt+1

(��t )�(��)1�� Pt

Yt+1Yt

#= (1�MCrt ) "; (33)

or

1� 'p

�t�

��t�1��(��)1��

� 1!

�t��t�1

��(��)1��

+

+'p�Et

�Ct+1Ct

�� " �t+1

(��t )�(��)1��

� 1!

�t+1

(��t )�(��)1��

Yt+1Yt

#= (1�MCrt ) ": (34)

20

6.3.2 Aggregation

The aggregate resource constraint is now simply given by

Yt = Ct +'p2

Pt�

��t�1��(��)1�� Pt�1

� 1!2Yt; (35)

or Yt =

1� 'p

2

�Pt

(��t�1)�(��)1��Pt�1

� 1�2!�1

Ct.

The aggregate production function hence is

Yt = N1��t : (36)

The aggregate real marginal costs are

MCrt =1

1� �Wt

PtY

�1��t :

6.3.3 Steady State

The deterministic steady state is obtained by dropping the time indices. Thesteady state in�ation is equal to the Central Bank in�ation target: � = ��:

The aggregate resource constraint implies

C =�1�

'p2

��1�

� � 1�2�

Y; (37)

from the aggregate production function

N = Y1

1�� ; (38)

and from real marginal costs

MCr =1

1� �W

PY

�1�� ; (39)

or WP = (1� �)MCrY ��

1�� :Equation (34) becomes�

1� 'p��1�

� � 1��1�

��+ 'p�

��1�

� � 1��1�

��= (1�MCrt ) "; (40)

then solving for the steady state value of aggregate real marginal costs yields

MCr ="� 1"

+(1� �)"

'p��1�

� � 1��1�

�: (41)

21

The markup, de�ned as 1MCr ; is therefore

markup =

�"� 1"

+(1� �)"

'p��1�

� � 1��1�

�

��1;

and the labor supply equation is

W

P= dnN

'C�; (42)

both in the case of �exible and real wage rigidity.Euler Equation gives

1 +�{ =1

�: (43)

(36), (39) and (42) imply

(1� �)MCrY ��

1�� = dnY'

1��Y �C�;

substituting the aggregate resource constraint, (37),

(1� �)MCrY ��

1�� = dnY'

1��Y ��1�

'p2

��1�

� � 1�2��

;

or

MCr =dn

(1� �)Y'

1��Y �Y�

1��1�

'p2

��1�

� � 1�2��

=dn

(1� �)Y'+�+�(1��)

1��1�

'p2

��1�

� � 1�2��

:

Combine it with real marginal costs in (41)

"� 1"+(1� �)"

'p��1�

� � 1� ��=

dn(1� �)Y

'+�+�(1��)1��

�1�

'p2

��1�

� � 1�2��

;

and then solve for Y

Y =

24 "�1" + (1��)

" 'p��1�

� � 1��1�

�

dn(1��)

�1� 'p

2 (��1�� 1)2

��35 1��'+�+�(1��)

; (44)

to get the steady state level of output.

22

Note that with Calvo price setting the steady state output is 8

Y =

0@x1+ "�1��

�"� 1"

� �1� ��

"1��

11��dns

' (1� ��"�1)

1A1��

'+�+�(1��)

:

We now consider the case in which price adjustment costs are rebated toconsumers. Market clearing conditions imply that the steady state house-hold budget constraint can be written as:

C =WN

P+�'p2

��1�

� � 1�2�

Y +� (45)

�rms steady state pro�ts are given by:

� = Y � WNP

��'p2

��1�

� � 1�2�

Y (46)

therefore, substituting (46) in (45) we get the steady state aggregate resourceconstraint which is,

C = Y; (47)

the steady state level of output becomes:

Y =

""�1" + (1��)

" 'p��1�

� � 1��1�

�

dn(1��)

# 1��'+�+�(1��)

(48)

6.3.4 The Long run Phillips Curve in the Rotemberg model

Y =

24 "�1" + (1��)

" 'p��1�

� � 1��1�

�

dn(1��)

�1� 'p

2 (��1�� 1)2

��35 1��'+�+�(1��)

; (49)

De�ne: a � "�1" ; b �

(1��)" 'p, c � dn

(1��) ; d �1��

'+�+�(1��) , which areconstants independent of the steady state in�ation rate ��: Then

dd��

0@" a+b(��1��1)��1�

�

c�1�'p

2 (��1��1)

2��#d1A = d

d�

�Y (��)d

�

= d [Y (��)]d�1b(2(1��)��1�2

��(1��)��)+��1�'p

2 (��1��1)

2��1('p(��1�

��1)(1��)��)

c�1�'p

2 (��1��1)

2��

8For a complete derivation of the Calvo model see Ascari and Merkl (2007).

23

= d [Y (��)]d�1b(1��)��(2��1�

��1)+��1�'p

2 (��1��1)

2��1('p(��1�

��1)(1��)��)

c�1�'p

2 (��1��1)

2��

This expression implies:- � = 1 =) dY

d�� = 0

- �� = 1 =) dYd�� > 0; so that the minimum of output occurs at negative

rate of steady state in�ation, unless � = 1; that implies b = 0.If � < 1; then

- 9�� < 1s:t:

8<:�� > �� =) dY

d�� > 0

�� = �� =) dYd�� = 0

�� < �� =) dYd�� < 0

24

7 Figures

0 1 2 3 4 5 6 73

2.5

2

1.5

1

0.5

0

0.5

Annualized Percentage Inflation Rate

Steady S tate Output(percentage deviation from the zero inflation steady state output)

Figure 1. Long-run Phillips Curve in the Calvo model

0 5 10 150

0.5

1

1.5

2Steady State Output:% deviation from zero inflation steady state

0 5 10 151.5

1

0.5

0

0.5Steady State Consumption:% deviation from zero inflation steady state

0 5 10 150

0.5

1

1.5

2Steady State Hours: % deviation from zero inflation steady state

0 5 10 152

1.5

1

0.5

0

0.5Steady State Welfare:% deviation from zero inflation steady state

Figure 2. Steady state in the Rotemberg model

25

0 5 10 151.2

1

0.8

0.6

0.4

0.2

0

0.2

Quarters

OUTPUT PATH (% dev. from new SS)

π = 4%

0 5 10 152.6

2.8

3

3.2

3.4

3.6

3.8

4

Quarters

INFLATION IN % (annualized)

π = 4%

0 5 10 158

8.5

9

9.5

10

10.5

Quarters

NOM. INTEREST RATE IN % (annualized)

π = 4%

0 5 10 152.5

2

1.5

1

0.5

0

Quarters

REAL WAGES (% dev. from new SS)

π = 4%

0 5 10 151.2

1

0.8

0.6

0.4

0.2

0

0.2

Quarters

CONSUMPTION (% dev. from new SS)

π = 4%

0 5 10 151.4

1.2

1

0.8

0.6

0.4

0.2

0

Quarters

HOURS (% dev. from new SS)

π = 4%

Figure 3. Temporary Shock to the Calvo Model

0 5 10 151.4

1.2

1

0.8

0.6

0.4

0.2

0

Quarters


π = 4%

0 5 10 152.4

2.6

2.8

3

3.2

3.4

3.6

3.8

4

Quarters


π = 4%

0 5 10 158.2

8.4

8.6

8.8

9

9.2

9.4

9.6

9.8

Quarters


π = 4%

0 5 10 152.5

2

1.5

1

0.5

0

Quarters

REAL MARG.COSTS (% dev. from new SS)

π = 4%

0 5 10 151

0.8

0.6

0.4

0.2

0

Quarters


π = 4%

0 5 10 151.4

1.2

1

0.8

0.6

0.4

0.2

0

Quarters


π = 4%

Figure 4. Temporary Shock to the Rotemberg Model

26

0 5 10 158

7

6

5

4

3

2

1

0

Quarters


π= 4%π = 6%π = 8%

0 5 10 150

1

2

3

4

5

6

7

8

Quarters


π= 4%π = 6%π = 8%

0 5 10 154

6

8

10

12

14

Quarters


π= 4%π = 6%π = 8%

0 5 10 158

6

4

2

0

2

4

6

Quarters


π= 4%π = 6%π = 8%

0 5 10 158

7

6

5

4

3

2

1

0

Quarters


π= 4%π = 6%π = 8%

0 5 10 150

1

2

3

4

5

6

7

Quarters


π= 4%π = 6%π = 8%

Figure 5. Permanent shock to the Calvo model

0 5 10 150.2

0

0.2

0.4

0.6

0.8

1

1.2

Quarters


π= 4%π = 6%π = 8%

0 5 10 152

0

2

4

6

8

Quarters


π= 4%π = 6%π = 8%

0 5 10 154

6

8

10

12

14

Quarters


π= 4%π = 6%π = 8%

0 5 10 150.05

0

0.05

0.1

0.15

0.2

0.25

0.3

Quarters


π= 4%π = 6%π = 8%

0 5 10 151

0.8

0.6

0.4

0.2

0

Quarters


π= 4%π = 6%π = 8%

0 5 10 150.2

0

0.2

0.4

0.6

0.8

1

1.2

Quarters


π= 4%π = 6%π = 8%

Figure 6. Permanent shock to the Rotemberg model

27

0 5 10 151

0.8

0.6

0.4

0.2

0

0.2

0.4

Quarters

OUTPUT PATH (%DEV. from NEW STEADY STATE)

γ = 0γ = 0.5γ = 0.9

0 5 10 150.8

0.6

0.4

0.2

0

0.2

0.4

0.6

Quarters

REAL WAGE (%DEV. from NEW STEADY STATE)

γ = 0γ = 0.5γ = 0.9

0 5 10 151

0

1

2

3

4

Quarters

INFLATION in% (ANNUALIZED)

γ = 0γ = 0.5γ = 0.9

0 5 10 153

4

5

6

7

8

9

Quarters

NOM. INTEREST RATE in% (ANNUALIZED)

γ = 0γ = 0.5γ = 0.9

Figure 7. Permanent shock to the Calvo model with real wage rigidity

0 5 10 150.05

0

0.05

0.1

0.15

0.2

0.25

0.3

Quarters

OUTPUT PATH (%DEV. from NEW STEADY STATE)

γ = 0γ = 0.5γ = 0.9

0 5 10 150.02

0

0.02

0.04

0.06

0.08

0.1

0.12

Quarters

REAL WAGE (%DEV. from NEW STEADY STATE)

γ = 0γ = 0.5γ = 0.9

0 5 10 150

1

2

3

4

Quarters

INFLATION in % (ANNUALIZED)

γ = 0γ = 0.5γ = 0.9

0 5 10 154

5

6

7

8

9

Quarters

NOM. INTEREST RATE in% (ANNUALIZED)

γ = 0γ = 0.5γ = 0.9

Figure 8. Permanent shock to the Rotemberg model with real wage rigidity

28

Elenco Quaderni già pubblicati

1. L. Giuriato, Problemi di sostenibilità di programmi di riforma strutturale, settembre 1993. 2. L. Giuriato, Mutamenti di regime e riforme: stabilità politica e comportamenti accomodanti, settembre 1993. 3. U. Galmarini, Income Tax Enforcement Policy with Risk Averse Agents, novembre 1993. 4. P. Giarda, Le competenze regionali nelle recenti proposte di riforma costituzionale, gennaio 1994. 5. L. Giuriato, Therapy by Consensus in Systemic Transformations: an Evolutionary Perspective, maggio 1994. 6. M. Bordignon, Federalismo, perequazione e competizione fiscale. Spunti di riflessione in merito alle ipotesi di riforma della finanza regionale in Italia, aprile 1995. 7. M. F. Ambrosanio, Contenimento del disavanzo pubblico e controllo delle retribuzioni nel pubblico impiego, maggio 1995. 8. M. Bordignon, On Measuring Inefficiency in Economies with Public Goods: an Overall Measure of the Deadweight Loss of the Public Sector, luglio 1995. 9. G. Colangelo, U. Galmarini, On the Pareto Ranking of Commodity Taxes in Oligopoly, novembre 1995. 10. U. Galmarini, Coefficienti presuntivi di reddito e politiche di accertamento fiscale, dicembre 1995. 11. U. Galmarini, On the Size of the Regressive Bias in Tax Enforcement, febbraio 1996. 12. G. Mastromatteo, Innovazione di Prodotto e Dimensione del Settore Pubblico nel Modello di Baumol, giugno 1996. 13. G. Turati, La tassazione delle attività finanziarie in Italia: verifiche empiriche in tema di efficienza e di equità, settembre 1996. 14. G. Mastromatteo, Economia monetaria post-keynesiana e rigidità dei tassi bancari, settembre 1996. 15. L. Rizzo, Equalization of Public Training Expenditure in a Cross-Border Labour Market, maggio 1997. 16. C. Bisogno, Il mercato del credito e la propensione al risparmio delle famiglie: aggiornamento di un lavoro di Jappelli e Pagano, maggio 1997.

17. F.G. Etro, Evasione delle imposte indirette in oligopolio. Incidenza e ottima tassazione, luglio 1997.

18. L. Colombo, Problemi di adozione tecnologica in un’industria monopolistica, ottobre 1997.

19. L. Rizzo, Local Provision of Training in a Common Labour Market, marzo 1998. 20. M.C. Chiuri, A Model for the Household Labour Supply: An Empirical Test On

A Sample of Italian Household with Pre-School Children, maggio 1998. 21. U. Galmarini, Tax Avoidance and Progressivity of the Income Tax in an

Occupational Choice Model, luglio 1998. 22. R. Hamaui, M. Ratti, The National Central Banks’ Role under EMU. The Case

of the Bank of Italy, novembre 1998.

23. A. Boitani, M. Damiani, Heterogeneous Agents, Indexation and the Non Neutrality of Money, marzo 1999. 24. A. Baglioni, Liquidity Risk and Market Power in Banking, luglio 1999. 25. M. Flavia Ambrosanio, Armonizzazione e concorrenza fiscale: la politica della Comunità Europea, luglio 1999.

26. A. Balestrino, U. Galmarini, Public Expenditure and Tax Avoidance, ottobre 1999.

27. L. Colombo, G. Weinrich, The Phillips Curve as a Long-Run Phenomenon in a Macroeconomic Model with Complex Dynamics, aprile 2000.

28. G.P. Barbetta, G. Turati, L’analisi dell’efficienza tecnica nel settore della sanità. Un’applicazione al caso della Lombardia, maggio 2000.

29. L. Colombo, Struttura finanziaria delle imprese, rinegoziazione del debito Vs. Liquidazione. Una rassegna della letteratura, maggio 2000.

30. M. Bordignon, Problems of Soft Budget Constraints in Intergovernmental Relationships: the Case of Italy, giugno 2000.

31. A. Boitani, M. Damiani, Strategic complementarity, near-rationality and coordination, giugno 2000.

32. P. Balduzzi, Sistemi pensionistici a ripartizione e a capitalizzazione: il caso cileno e le implicazioni per l’Italia, luglio 2000.

33. A. Baglioni, Multiple Banking Relationships: competition among “inside” banks, ottobre 2000.

34. A. Baglioni, R. Hamaui, The Choice among Alternative Payment Systems: The European Experience, ottobre 2000.

35. M.F. Ambrosanio, M. Bordignon, La concorrenza fiscale in Europa: evidenze, dibattito, politiche, novembre 2000.

36. L. Rizzo, Equalization and Fiscal Competition: Theory and Evidence, maggio 2001.

37. L. Rizzo, Le Inefficienze del Decentramento Fiscale, maggio 2001. 38. L. Colombo, On the Role of Spillover Effects in Technology Adoption Problems,

maggio 2001. 39. L. Colombo, G. Coltro, La misurazione della produttività: evidenza empirica e

problemi metodologici, maggio 2001. 40. L. Cappellari, G. Turati, Volunteer Labour Supply: The Role of Workers’

Motivations, luglio 2001. 41. G.P. Barbetta, G. Turati, Efficiency of junior high schools and the role of

proprietary structure, ottobre 2001. 42. A. Boitani, C. Cambini, Regolazione incentivante per i servizi di trasporto

locale, novembre 2001. 43. P. Giarda, Fiscal federalism in the Italian Constitution: the aftermath of the

October 7th referendum, novembre 2001. 44. M. Bordignon, F. Cerniglia, F. Revelli, In Search for Yardstick Competition:

Property Tax Rates and Electoral Behavior in Italian Cities, marzo 2002. 45. F. Etro, International Policy Coordination with Economic Unions, marzo 2002. 46. Z. Rotondi, G. Vaciago, A Puzzle Solved: the Euro is the D.Mark, settembre

2002. 47. A. Baglioni, Bank Capital Regulation and Monetary Policy Transmission: an

heterogeneous agents approach, ottobre 2002. 48. A. Baglioni, The New Basle Accord: Which Implications for Monetary Policy

Transmission?, ottobre 2002. 49. F. Etro, P. Giarda, Redistribution, Decentralization and Constitutional Rules,

ottobre 2002. 50. L. Colombo, G. Turati, La Dimensione Territoriale nei Processi di

Concentrazione dell’Industria Bancaria Italiana, novembre 2002.

51. Z. Rotondi, G. Vaciago, The Reputation of a newborn Central Bank, marzo 2003.

52. M. Bordignon, L. Colombo, U. Galmarini, Fiscal Federalism and Endogenous Lobbies’ Formation, ottobre 2003.

53. Z. Rotondi, G. Vaciago, The Reaction of central banks to Stock Markets, novembre 2003.

54. A. Boitani, C. Cambini, Le gare per i servizi di trasporto locale in Europa e in Italia: molto rumore per nulla?, febbraio 2004.

55. V. Oppedisano, I buoni scuola: un’analisi teorica e un esperimento empirico sulla realtà lombarda, aprile 2004.

56. M. F. Ambrosanio, Il ruolo degli enti locali per lo sviluppo sostenibile: prime valutazioni, luglio 2004.

57. M. F. Ambrosanio, M. S. Caroppo, The Response of Tax Havens to Initiatives Against Harmful Tax Competition: Formal Statements and Concrete Policies, ottobre 2004.

58. A. Monticini, G. Vaciago, Are Europe’s Interest Rates led by FED Announcements?, dicembre 2004.

59. A. Prandini, P. Ranci, The Privatisation Process, dicembre 2004. 60. G. Mastromatteo, L. Ventura, Fundamentals, beliefs, and the origin of money: a

search theoretic perspective, dicembre 2004. 61. A. Baglioni, L. Colombo, Managers’ Compensation and Misreporting, dicembre

2004. 62. P. Giarda, Decentralization and intergovernmental fiscal relations in Italy: a

review of past and recent trends, gennaio 2005. 63. A. Baglioni, A. Monticini, The Intraday price of money: evidence from the e-

MID market, luglio 2005. 64. A. Terzi, International Financial Instability in a World of Currencies Hierarchy,

ottobre 2005. 65. M. F. Ambrosanio, A. Fontana, Ricognizione delle Fonti Informative sulla

Finanza Pubblica Italiana, gennaio 2006. 66. L. Colombo, M. Grillo, Collusion when the Number of Firms is Large, marzo

2006. 67. A. Terzi, G. Verga, Stock-bond correlation and the bond quality ratio: Removing

the discount factor to generate a “deflated” stock index, luglio 2006. 68. M. Grillo, The Theory and Practice of Antitrust. A perspective in the history of

economic ideas, settembre 2006. 69. A. Baglioni, Entry into a network industry: consumers’ expectations and firms’

pricing policies, novembre 2006. 70. Z. Rotondi, G. Vaciago, Lessons from the ECB experience: Frankfurt still

matters!, marzo 2007. 71. G. Vaciago, Gli immobili pubblici…..ovvero, purché restino immobili, marzo

2007. 72. F. Mattesini, L. Rossi, Productivity shocks and Optimal Monetary Policy in a

Unionized Labor Market Economy, marzo 2007. 73. L. Colombo, G. Femminis, The Social Value of Public Information with Costly

Information Acquisition, marzo 2007. 74. L. Colombo, H. Dawid, K. Kabus, When do Thick Venture Capital Markets

Foster Innovation? An Evolutionary Analysis, marzo 2007. 75. A. Baglioni, Corporate Governance as a Commitment and Signalling Device,

novembre 2007. 76. L. Colombo, G. Turati, The Role of the Local Business Environment in Banking

Consolidation, febbraio 2008.

77. F. Mattesini, L. Rossi, Optimal Monetary Policy in Economies with Dual Labor Markets, febbraio 2008.

78. M. Abbritti, A. Boitani, M. Damiani, Labour market imperfections, “divine coincidence” and the volatility of employment and inflation, marzo 2008.

79. S. Colombo, Discriminatory prices, endogenous locations and the Prisoner Dilemma problem, aprile 2008.

80. L. Colombo, H. Dawid, Complementary Assets, Start-Ups and Incentives to Innovate, aprile 2008.

81. A. Baglioni, Shareholders’ Agreements and Voting Power, Evidence from Italian Listed Firms, maggio 2008.

82. G. Ascari, L. Rossi, Long-run Phillips Curve and Disinflation Dynamics: Calvo vs. Rotemberg Price Setting, settembre 2008.

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